densityf_Poincare.tex

The sorted version of $f$ admits a $\sigma$-finite invariant measure which is
absolutely continuous with respect to Lebesgue measure and its density is
known \cite{schweiger,MR1336331}.

%The density function of the invariant measure of $f:\Delta\to\Delta$ for
%the (sorted?) Poincar\'e algorithm is \cite{schweiger}
%\[
%\frac{1}{x_{\pi 0}(x_{\pi 0}+x_{\pi 1})(x_{\pi 0}+x_{\pi 1}+x_{\pi 2})}
%\]
%on the part $\mathbf{x}=(x_1,x_2,x_3)\in\Lambda_\pi\cap\Delta$.